how many periods of the function y = tan x are there between -\\frac{5\\pi}{2} and \\frac{7\\pi}{2}?
how many periods of the function y = tan x are there between -\\frac{5\\pi}{2} and \\frac{7\\pi}{2}?
Answer
Answer:
3
Explanation:
Step1: Recall period of tangent function
The period of $y = \tan x$ is $\pi$.
Step2: Calculate the length of the interval
The length of the interval from $-\frac{5\pi}{2}$ to $\frac{7\pi}{2}$ is $\frac{7\pi}{2}-\left(-\frac{5\pi}{2}\right)=\frac{7\pi + 5\pi}{2}=6\pi$.
Step3: Divide by the period
To find the number of periods, divide the length of the interval by the period of the function. So, $\frac{6\pi}{\pi}=6$. But we need to consider the non - overlapping periods. The number of full periods of $y = \tan x$ in the open - interval $\left(-\frac{5\pi}{2},\frac{7\pi}{2}\right)$ is 3.